details

property	value
status	complete
benchmark	#4.27.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n037.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.273984909058 seconds
cpu usage	0.267907086
max memory	1.3484032E7

stage attributes

key	value
output-size	1620
starexec-result	MAYBE

output

/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o false : [] --> o if : [o * o * o] --> o le : [o * o] --> o minus : [o * o] --> o p : [o] --> o s : [o] --> o true : [] --> o p(0) => 0 p(s(X)) => X le(0, X) => true le(s(X), 0) => false le(s(X), s(Y)) => le(X, Y) minus(X, 0) => X minus(X, s(Y)) => if(le(X, s(Y)), 0, p(minus(X, p(s(Y))))) if(true, X, Y) => X if(false, X, Y) => Y As the system is orthogonal, it is terminating if it is innermost terminating by [Gra95]. Then, by [FuhGieParSchSwi11], it suffices to prove (innermost) termination of the typed system, with sort annotations chosen to respect the rules, as follows: 0 : [] --> bc false : [] --> ib if : [ib * bc * bc] --> bc le : [bc * bc] --> ib minus : [bc * bc] --> bc p : [bc] --> bc s : [bc] --> bc true : [] --> ib +++ Citations +++ [FuhGieParSchSwi11] C. Fuhs, J. Giesl, M. Parting, P. Schneider-Kamp, and S. Swiderski. Proving Termination by Dependency Pairs and Inductive Theorem Proving. In volume 47(2) of Journal of Automated Reasoning. 133--160, 2011. [Gra95] B. Gramlich. Abstract Relations Between Restricted Termination and Confluence Properties of Rewrite Systems. In volume 24(1-2) of Fundamentae Informaticae. 3--23, 1995. popout

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all output return to TRS Stand 20472